正数量曲率与真作用量的Poincare对偶
Positive Scalar Curvature and Poincare Duality for Proper Actions
摘要：
对几乎连通李群G，研究了正常余紧作用的G-等变指标理论及其应用，包括正数量曲率的G-不变黎曼度量的存在性和对G-不变黎曼度量的限制.我们证明了刚性的结果殆复流形，推广服部的结果，和一个类似的Petrie猜想。当G是几乎连通李群或离散群时，我们建立了G-等变K-同调与K-理论之间的Poincare对偶，指出Poincare对偶对一般G不一定成立.
英文摘要：
For G an almost-connected Lie group, we study G-equivariant index theory for proper co-compact actions with various applications, including obstructions to and existence of G-invariant Riemannian metrics of positive scalar curvature. We prove a rigidity result for almost-complex manifolds, generalising Hattori's results, and an analogue of Petrie's conjecture. When G is an almost-connected Lie group or a discrete group, we establish Poincare duality between G-equivariant K-homology and K-theory, observing that Poincare duality does not necessarily hold for general G.
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